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梦梦 · 2025年06月12日

关于回归的的a和b

  1. FRM II
  2. Risk Management And Investment Management

NO.PZ2023101902000045

问题如下：

Rick Masler is considering the performance of the managers of two funds, the HCM Fund and the GRT Fund. He uses a linear regression of each manager’s excess returns (ri) against the excess returns of a peer group (rB): ri = ai + bi * rB +ei The information he compiles is as follows:


Based on this information, which of the following statements is correct?

选项：

A.The regression suggests that both managers have greater skill than the peer group.

B.The ai term measures the extent to which the manager employs greater or lesser amounts of leverage than do his/her peers.

C.If the GRT Fund were to lose 10% in the next period, the return on equity (ROE) would be -60%.

D.The sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund.

解释：

Statement d is correct as can be seen from the b coefficient. It. is higher for GRT and lower for HCM. This indicates that the sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund.

老师好，1、这里听了视频还是没太理解为什么b是代表杠杆率？b是benchmark变动1个单位，收益率变动多少，但是变动大就代表我杠杆大的逻辑是什么？那b如果是0.0001呢？b有可能是负值吗？负值代表什么意思？

2、为什么b大但是a却小？大盘涨1，GRT上涨3.45，那为什么a会小呢，应该a大吧，这块儿也不是很明白

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1 个答案

李坏_品职助教 · 2025年06月12日

嗨，努力学习的PZer你好：


He uses a linear regression of each manager’s excess returns (ri) against the excess returns of a peer group (rB)


这句话的意思是，回归模型里面的ri（因变量）是基金经理的超额收益率，而自变量rB是同行业的平均收益率。 如果b很大(假设b = 10)，说明当行业内平均收益变化1个点的时候，这个基金经理的收益会变化10%，这是很剧烈的波动了。 所以b越大，说明基金经理的波动越剧烈，杠杆越大。


b有可能是负数，但是概率比较小。假设b是-1，就说明这个基金经理与行业内平均收益是反向变化的，很少见。


a是线性回归模型里面的常数项，而b是斜率项，这俩并没有必然的大小联系。a和b都是最小二乘法算出来的结果，取决于历史数据的情况，a和b之间没有必然的大小关系。

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2025-08-04 10:18 1 · 回答